anonymous
  • anonymous
Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <7, 2>, v = <21, 6>
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
let u and v be two vectors they are orthogonal if and only if u dot v = 0 ------------------------------------------------------- they are parallel if and only if v = k*u where k is some scalar
anonymous
  • anonymous
ok so how do i find u dot v
jim_thompson5910
  • jim_thompson5910
u = v = u dot v = a*c + b*d the * means multiplication between two scalars u,v are vectors a,b,c,d are scalars

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jim_thompson5910
  • jim_thompson5910
example u = <2,3> v = <7,9> u dot v = 2*7 + 3*9 = 14 + 27 = 41
jim_thompson5910
  • jim_thompson5910
"dot" refers to the dot product of two vectors
anonymous
  • anonymous
Ok so for my problem u dot v = 159.
jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • jim_thompson5910
since that result isn't 0, the vectors aren't orthogonal
anonymous
  • anonymous
How would I determine if they are parallel or not?
jim_thompson5910
  • jim_thompson5910
can you find some scalar k that makes v = k*u true?
jim_thompson5910
  • jim_thompson5910
does k = 5 make v = k*u true? ie is v = 5*u true?
jim_thompson5910
  • jim_thompson5910
Alternate method Let u = v = u and v are parallel if and only if a/c = b/d is true
anonymous
  • anonymous
Okay I got 7/ 21 = 2/6 so they are parallel, thanks!
jim_thompson5910
  • jim_thompson5910
yep they are parallel

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